Higher order Ambrosio–Tortorelli scheme with non-negative spatially dependent parameters

Abstract

Abstract The Ambrosio–Tortorelli approximation scheme with weighted underlying metric is investigated. It is shown that it Γ-converges to a Mumford–Shah image segmentation functional depending on the weight ω ⁢ d ⁢ x {\omega\,dx} , where ω is a special function of bounded variation, and on its values at the jumps.